Physics

Thermal Properties and Thermodynamics

431 Questions

Thermal properties and thermodynamics questions evaluate concepts of heat transfer, thermal efficiency, and temperature variations. Problems involve calculating heat content, conductivity, and the performance of heat engines. This subject is regularly tested in physics sections across multiple competitive platforms.

Heat transfer calculationsThermal efficiencyBlack body radiationTemperature variationsRefrigeration performance

Thermal Properties and Thermodynamics Questions

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The temperature of a piece of metal is raised from $27^oC$ to $51.2^oC$. The rate at which the metal radiates energy increases nearly

  1. 1.36 times

  2. 2 times

  3. 4 times

  4. 8 times
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rate at which a substance radiates is directly proportional to the fourth power of the absolute temperature.
The temperature increases from $300K$ to $324.2K$ which is an increase by $1.080$
Hence the rate at which the metal radiates would increase by $(1.08)^{4}$ = $1.36$

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A black body at a temperature $77^oC$ radiates heat at a rate of $10 calcm^{-2}s^{-1}$. The rate at which this body would radiate heat in units of $cal \ cm^{-2} \ s^{-1}$ at $427^oC$ is closest to:

  1. 40

  2. 160

  3. 200

  4. 400
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Energy radiated $P=\sigma AT^4$
$ \displaystyle \frac{P _1}{P _2} = \cfrac{T _1^4}{T _2^4}= { \bigg ( \frac {350}{700} \bigg ) }^4 = \frac{10}{P _2} \space or P _2 = 160$

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The temperature of a black body corresponding to which it will emit energy at the rate of $1 watt/cm^2$ will be

  1. 650K

  2. 450K

  3. 350K

  4. 250K
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$E\propto { T }^{ 4 }\quad \Longrightarrow \quad E=\sigma { T }^{ 4 }$
$\sigma =5.67*{ 10 }^{ 8 }W{ m }^{ 2 }{ k }^{ 4 }$
$1*{ 10 }^{ -4 }=5.67*{ 10 }^{ 8 }*{ T }^{ 4 }$
$T=648k\cong 650k$



Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The solar constant for the earth is $\Sigma$. The surface temperature of the sun is $T$ K. The sun subtends an angle $\theta$ at the earth

  1. $\Sigma \space \propto \space T^4$
  2. $\Sigma \space \propto \space T^2$
  3. $\Sigma \space \propto \space \theta^4$
  4. $\Sigma \space \propto \space \theta$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By Stephan Boltzman law,


$P=\sigma (4\pi { R }^{ 2 }){ T }^{ 4 }$

$\theta =\dfrac { 2r }{ R } $ where R is distance between earth and sun and r is radius of earth.

Hence, $\sum {  } =\dfrac { P }{ 4\pi { r }^{ 2 } } =C{ T }^{ 4 }{ \left( \dfrac { R }{ r }  \right)  }^{ 2 }=K{ T }^{ 4 }{ \theta  }^{ 2 }$

Hence $\sum {  } \alpha { T }^{ 4 }$ and $\sum {  } \alpha { \theta }^{ 2 }$

Answer is option A.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

There are two planets $A$ and $B$ at a large distance Planet $A$ is bigger and hotter than planet $B$. The angular diameter of planet $A$ is $40$ minute of arc as seen from planet $B$. The energy received by planet $B$ is $3cal-cm^{-2}$ per minute. Assuming the radiation to be black body in character. Given that stefan costant is $5.67\times 10^{-8}\ Wm^{-2}\ K^{-4}$. The temperature of planet $A$ is

  1. $(10.93\times 10^{14})^{1/4}\ K$
  2. $(53.21\times 10^{14})^{1/4}\ K$
  3. $(63.63\times 10^{14})^{1/4}\ K$
  4. $(63.21\times 10^{14})^{1/4}\ K$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The energy received by planet B is given by the Stefan-Boltzmann law applied to the radiation from A reaching B. Using the angular diameter and the flux, one can determine the temperature of A.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A blackened steel plate is put in a dark room after being heated up to a high temperature. A white spot on the plate appears. 

  1. brighter than the plate

  2. as bright as the plate

  3. dull as compared to the plate

  4. appears to be yellow
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Kirchhoff's law of radiation, good absorbers are good emitters. A white spot (which is a poor absorber/emitter compared to the blackened surface) will emit less radiation at the same temperature, making it appear darker or less bright than the surrounding blackened surface.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Solar constant for earth is $2 \mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 } ,$ if distance ofmerary from sun is 0.4 times than distance of earthfrom sun then solar constant for mercury will be? 

  1. 12.5$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$
  2. 25$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$
  3. 0.32$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$
  4. 2$\mathrm { cal } / \mathrm { min } \mathrm { cm } ^ { 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Choose the correct relation, when the temperature of an isolated black body falls from $T _{1}$ to $T _{2}$ in time $'t'$, and assume $'c'$ to be a constant.

  1. $t - c \left (\dfrac {1}{T _{2}} - \dfrac {1}{T _{1}}\right )$
  2. $t = c \left (\dfrac {1}{T _{2}^{2}} - \dfrac {1}{T _{1}^{2}}\right )$
  3. $t = c \left (\dfrac {1}{T _{2}^{3}} - \dfrac {1}{T _{1}^{3}}\right )$
  4. $t = c \left (\dfrac {1}{T _{2}^{4}} - \dfrac {1}{T _{1}^{4}}\right )$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Stefan-Boltzmann law, the rate of cooling is dQ/dt = -sigma * A * T^4. Since dQ = mc * dT, we have mc * dT/dt = -sigma * A * T^4. Separating variables, T^-4 * dT = -(sigma * A / mc) * dt. Integrating gives (1/3) * T^-3 = (sigma * A / mc) * t. Thus t is proportional to (1/T2^3 - 1/T1^3).

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Calculate the surface temperature of the planet, if the energy radiated by unit area in unit time is $5.67 \times 10^4$ watt.

  1. $1273^{\circ}C$
  2. $1000^{\circ}C$
  3. $727^{\circ}C$

  4. 727K
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to stefan's Boltzmann law, the energy radiated per unit time:
$E=\sigma A{ T }^{ 4 }$
It is given that: ${E}={5.67}\times{10}^{4}$
Therefore, ${5.67}\times{10}^{4}={5.67}\times{10}^{-8}\times1\times{T}^{4}$
So, ${T}={1000}K$
${T}={1000-273}={727} \  ^oC$

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A hot liquid is kept in a big room . the logarithm of the numerical value of the temperature difference between the liquid and the room is plotted against time. the plot will be very nearly

  1. a straight line

  2. a circular arc

  3. a parabola

  4. an ellipse
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to Newton's law of cooling, dT/dt = -k(T - T_room). Integrating this gives ln(T - T_room) = -kt + C. Thus, the plot of the logarithm of the temperature difference versus time is a straight line.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A solid at temperature $ T _1 $ is kept in an evacuated chamber at Temperature $ T _2 > T _1 $ . the rate of increase of temperature of the body is proportional to

  1. $ T _2- T _1 $
  2. $ T^2 _2 - T^2 _1 $
  3. $ T^3 _2 -T^3 _1 $
  4. $ T^4 _1 - T^4 _1 $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The rate of heat exchange for a body at temperature T1 in a chamber at T2 is proportional to the difference in the fourth powers of the temperatures (T2^4 - T1^4) due to radiative heat transfer.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A black body radiates energy at the rate of $E$ watt per metr$e^2$ at a high ternperature $T$ K. when the temperature is reduced to $(T/2)$ K, the radiant energy will be

  1. $E/16$
  2. $E/4$
  3. $E/2$
  4. $2E$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By Stefan-Boltzmann law black body radiation of energy $E$ is directly proportional to fourth power of $T$ temperature of the black body.
$E\quad \propto \quad { T }^{ 4 }$
If the temperature of the body is reduced to $\dfrac{T}{2}$, the energy of radiation will be $\dfrac{E}{16}$
option (A) is the correct answer.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

The temperature of a spherical planet is related to the distance from sun as :

  1. $T \propto 1/d^{2}$
  2. $T\propto \dfrac{1}{\sqrt{d}}$
  3. $T\propto d$
  4. $T\propto d^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
A planet reaches its equilibrium temperature when the amount of heat it absorbs from the sun is equal to the amount that it radiates back to space.
The energy absorbed is equal to the insolation at planet's distance (which is Sun's bolometric output divided by $4\pi$ times the distance squared) times the planet's profile area times the planet's Bond aldedo. The amount radiated (assuming that the thermal radiation is approximately black body radiation) is proportional to the planet's surface area times its emmisivity times the forth power of its temperature.

Now, throwing away 2, $\pi$ and other constants that do not vary with temperature or distance.
${ T }^{ 4 }\alpha \cfrac { 1 }{ { d }^{ 2 } } \\ \Rightarrow T\alpha \cfrac { 1 }{ \sqrt { d }  } $
Multiple choice stefan's law black body radiation heat transfer thermal properties physics

Three bodies A, B, C are at $-27^{o}$C, $0^{o}$C, $100^{o}$C respectively. The body which does not radiate heat is:

  1. A

  2. B

  3. none as all the bodies radiate heat

  4. C
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

All bodies radiate heat irrespective of temperature.
Heat radiated per unit time is given by Stefan's law.

Multiple choice stefan's law black body radiation heat transfer thermal properties physics

A solid shpere and a hollow sphere of the same material and of equal radii are heated to the same temperature

  1. both will emit equal amount of radiation per unit time in the beginning.

  2. both will absorbs equal amount of radiation per second from the surrounding in the beginning.

  3. the initial rate of cooling will be the same for both the spheres

  4. the two spheres will have equal temperature at any instant
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation

According to many radiation laws like Stefan Boltzmann we know that radiation emission and absorption are a purely surface phenomenon. Since the two bodies are of same material, same radii, and same temperature they will at that instant radiate and absorb at the same rates.
But however since the hollow sphere has lesser mass, the rate at which it's temperature will rise will be different from that of the solid sphere. Hence their rates of cooling would be varied and they would have different temperatures at different times.